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Qutrit Rotations #2 (TRY) (#2846)
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* Adding tests for tensor observables

* Added tests for tensor sample

* Updated tests

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* Partition device apply ops test case.

* Run black

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* Added tests for controlled qutrit unitary

* Fix broadcasting, finish tests for CQutritUnitary

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* Added tests for updated utils.sparse_hamiltonian

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* Updated TRY and tests

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---------

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@mudit2812 @glassnotes
@Jaybsoni @albi3ro @timmysilv
6 people authored May 23, 2023
1 parent 2bb11ce commit 53560ad
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4 changes: 4 additions & 0 deletions doc/releases/changelog-dev.md
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Expand Up @@ -12,6 +12,10 @@
given subspace.
[(#2845)](https://github.com/PennyLaneAI/pennylane/pull/2845)

* Added the `TRY` qutrit rotation operator, which allows applying a Y rotation on a
given subspace.
[(#2846)](https://github.com/PennyLaneAI/pennylane/pull/2846)

<h3>Improvements 🛠</h3>

* `DiagonalQubitUnitary` now decomposes into `RZ`, `IsingZZ` and `MultiRZ` gates
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1 change: 1 addition & 0 deletions pennylane/devices/default_qutrit.py
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Expand Up @@ -62,6 +62,7 @@ class DefaultQutrit(QutritDevice):
"TSWAP",
"THadamard",
"TRX",
"TRY",
}

# Identity is supported as an observable for qml.state() to work correctly. However, any
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1 change: 1 addition & 0 deletions pennylane/ops/qutrit/__init__.py
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Expand Up @@ -37,6 +37,7 @@
"TSWAP",
"THadamard",
"TRX",
"TRY",
}

obs = {
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152 changes: 148 additions & 4 deletions pennylane/ops/qutrit/parametric_ops.py
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Expand Up @@ -99,13 +99,13 @@ def __init__(self, phi, wires, subspace=(0, 1), do_queue=True, id=None):

@property
def subspace(self):
"""The single-qutrit basis states the operator acts on.
"""The single-qutrit basis states which the operator acts on
The subspace defines which two basis states the opreation acts on. The basis state
not included in the subspace remains unaffected.
This subspace determines which two single-qutrit basis states the operator acts on.
The remaining basis state is not affected by the operator.
Returns:
tuple[int]: subspace on which the operator acts
tuple[int]: subspace on which operator acts
"""
return self._subspace

Expand Down Expand Up @@ -169,3 +169,147 @@ def adjoint(self):

def pow(self, z):
return [TRX(self.data[0] * z, wires=self.wires, subspace=self.subspace)]


class TRY(Operation):
r"""
The single qutrit Y rotation
Performs the RY operation on the specified 2D subspace. The subspace is
given as a keyword argument and determines which two of three single-qutrit
basis states the operation applies to.
The construction of this operator is based on section 3 of
`Di et al. (2012) <https://arxiv.org/abs/1105.5485>`_.
.. math:: TR_y^{jk}(\phi) = \exp(-i\phi\sigma_y^{jk}/2),
\sigma_y^{jk} = -i |j\rangle\langle k| + i |k\rangle\langle j|,
j, k \in \{0, 1, 2\}, j \neq k
**Details:**
* Number of wires: 1
* Number of parameters: 1
* Number of dimensions per parameter: (0,)
Args:
phi (float): rotation angle :math:`\phi`
wires (Sequence[int] or int): the wire the operation acts on
subspace (Sequence[int]): the 2D subspace on which to apply operation
do_queue (bool): Indicates whether the operator should be
immediately pushed into the Operator queue (optional)
id (str or None): String representing the operation (optional)
**Example**
The specified subspace will determine which basis states the operation actually
applies to:
>>> qml.TRY(0.5, wires=0, subspace=[0, 1]).matrix()
array([[ 0.96891242+0.j, -0.24740396-0.j, 0. +0.j],
[ 0.24740396+0.j, 0.96891242+0.j, 0. +0.j],
[ 0. +0.j, 0. +0.j, 1. +0.j]])
>>> qml.TRY(0.5, wires=0, subspace=[0, 2]).matrix()
array([[ 0.96891242+0.j, 0. +0.j, -0.24740396-0.j],
[ 0. +0.j, 1. +0.j, 0. +0.j],
[ 0.24740396+0.j, 0. +0.j, 0.96891242+0.j]])
>>> qml.TRY(0.5, wires=0, subspace=[1, 2]).matrix()
array([[ 1. +0.j, 0. +0.j, 0. +0.j],
[ 0. +0.j, 0.96891242+0.j, -0.24740396-0.j],
[ 0. +0.j, 0.24740396+0.j, 0.96891242+0.j]])
"""
num_wires = 1
num_params = 1
"""int: Number of trainable parameters that the operator depends on."""

ndim_params = (0,)
"""tuple[int]: Number of dimensions per trainable parameter that the operator depends on."""

grad_method = "A"
parameter_frequencies = [(0.5, 1)]

# Internal dictionary to map subpsaces to Gell-Mann observable for the generator
_index_dict = {(0, 1): 2, (0, 2): 5, (1, 2): 7}

def generator(self):
return qml.s_prod(-0.5, qml.GellMann(self.wires, index=self._index_dict[self.subspace]))

def __init__(self, phi, wires, subspace=(0, 1), do_queue=True, id=None):
self._subspace = self.validate_subspace(subspace)
self._hyperparameters = {
"subspace": self._subspace,
}
super().__init__(phi, wires=wires, do_queue=do_queue, id=id)

@property
def subspace(self):
"""The single-qutrit basis states which the operator acts on
This subspace determines which two single-qutrit basis states the operator acts on.
The remaining basis state is not affected by the operator.
Returns:
tuple[int]: subspace on which operator acts
"""
return self._subspace

@staticmethod
def compute_matrix(theta, subspace=(0, 1)): # pylint: disable=arguments-differ
r"""Representation of the operator as a canonical matrix in the computational basis (static method).
The canonical matrix is the textbook matrix representation that does not consider wires.
Implicitly, this assumes that the wires of the operator correspond to the global wire order.
.. seealso:: :meth:`~.TRY.matrix`
Args:
theta (tensor_like or float): rotation angle
subspace (Sequence[int]): the 2D subspace on which to apply operation
Returns:
tensor_like: canonical matrix
**Example**
>>> qml.TRY.compute_matrix(torch.tensor(0.5), subspace=[0, 2])
tensor([[ 0.9689+0.j, 0.0000+0.j, -0.2474-0.j],
[ 0.0000+0.j, 1.0000+0.j, 0.0000+0.j],
[ 0.2474+0.j, 0.0000+0.j, 0.9689+0.j]])
"""
c = qml.math.cos(theta / 2)
s = qml.math.sin(theta / 2)

if qml.math.get_interface(theta) == "tensorflow":
c = qml.math.cast_like(c, 1j)
s = qml.math.cast_like(s, 1j)

# The following avoids casting an imaginary quantity to reals when backpropagating
c = (1 + 0j) * c
s = (1 + 0j) * s

shape = qml.math.shape(theta)
is_broadcasted = len(shape) != 0 and shape[0] > 1
# Construct identity matrices and cast to complex type
mat = (
qml.math.tensordot([1] * qml.math.shape(theta)[0], qml.math.eye(3), axes=0)
if is_broadcasted
else qml.math.eye(3)
)
mat = qml.math.cast_like(mat, s)
slices = tuple(itertools.product(subspace, subspace))
if is_broadcasted:
slices = [(Ellipsis, *s) for s in slices]

# Put rotation terms in the appropriate indices using the slices
mat[slices[0]] = mat[slices[3]] = c
mat[slices[1]] = -s
mat[slices[2]] = s
return qml.math.convert_like(mat, theta)

def adjoint(self):
return TRY(-self.data[0], wires=self.wires, subspace=self.subspace)

def pow(self, z):
return [TRY(self.data[0] * z, wires=self.wires, subspace=self.subspace)]
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